On the Polarized Absorption Lines in Gamma-ray Burst Optical Afterglows

Spectropolarimetric measurements of gamma-ray burst (GRB) optical afterglows contain polarization information for both continuum and absorption lines. Based on the Zeeman effect, an absorption line in a strong magnetic field is polarized and split into a triplet. In this paper, we solve the polarization radiative transfer equations of the absorption lines, and obtain the degree of linear polarization of the absorption lines as a function of the optical depth. In order to effectively measure the degree of linear polarization for the absorption lines, a magnetic field strength of at least $10^3$ G is required. The metal elements that produce the polarized absorption lines should be sufficiently abundant and have large oscillation strengths or Einstein absorption coefficients. We encourage both polarization measurements and high-dispersion observations of the absorption lines in order to detect the triplet structure in early GRB optical afterglows.